You are the fire control officer for B Battery, 503rd Air Defense Artillery (firing the ARROW antiballistic missile) stationed on the northwestern most island of Hawaii, Kauai. As part of the United States Strategic Defense Initiative (SDI - also known as Star Wars), your battery's mission is to protect the US mainland by destroying any incoming ballistic missiles launched from Asia.
On February 11, 2008, you are on duty when you receive satellite information that the North Koreans have launched a "RED WIND" ICBM (intercontinental ballistic missile) from their launch facility at No-dong (N40°51'17", E129°39'58") aimed at the Hawaiian Islands (instead of at the continental US)! You immediately prepare the battery to destroy this missile since the consequences could be very negative.
A few minutes later your radars report acquiring the incoming missile information ( t = 0 seconds is time of acquisition):
The ARROW Missile
Altitude: 127,157 meters at t = 0 seconds
Downward velocity: 943.113 m/sec at t = 5 seconds
You know the following times are required before firing: 22 seconds to swing the missiles into firing position, an additional 3 seconds to input firing data, and then one additional second to affect rocket motor startup and launch. Since the incoming missile has been targeted for your position (apparently), it is imperative that it be shot down. Also, you know that the missile is probably tipped with a weapon of mass destruction (nuclear?) so it must be destroyed at least 13 km from your position (why?).
EQ 1
You know the missile is falling ballistically (affected only by gravity) and its height as a function of time, h(t), in seconds can be predicted by the equation 1 shown to the right. Other parameters include: g is the acceleration due to gravity ( 9.807 m/sec2 ), vo is it's initial velocity at t = 0, and so is its altitude at t= 0.
You also know the ARROW missile launches with a velocity of 3300 mi/hour and that the motor cuts out immediately after launch with small rockets making adjustments to impact the target. Since the ARROW missile is essentially a ballistic missile and obeys the same ballistic equation (EQ 1 shown above).

Determine: (1) the earliest time (in seconds after t = 0) your battery will be able to intercept the incoming missile, (2) the time and altitude of this earliest interception, and (3) the latest launch time to destroy the missile at the 13 km minimum altitude.
Provide your answers in a professional, word processed report with all supporting documentation, calculations, and graphs.